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Topic: Lost in the woods (Read 1467 times) |
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mallman
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Lost in the woods
« on: Apr 3rd, 2006, 10:17pm » |
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You are in a thick wooded forest (no compass/GPS). There is a road one mile away, in an unknown direction. What is the shortest distance you can walk in order to reach the road.
Hint: More than one mile, less than 6.2 miles.
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| « Last Edit: Apr 24th, 2006, 6:20pm by mallman » |
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rmsgrey
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Re: Lost in the woods
« Reply #1 on: Apr 4th, 2006, 5:55am » |
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This thread has already explored a very similar riddle (the difference is that that one's got boundaries on two sides not just one)
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SMQ
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Re: Lost in the woods
« Reply #2 on: Apr 4th, 2006, 6:04am » |
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on Apr 3rd, 2006, 10:17pm, mallman wrote:| Hint: More than one mile less than 6.2 miles. |
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You sure about that? I don't see a way to do better than [sqrt]3 + 7[pi]/6 + 1 ~= 6.397 miles.
To arrive at that figure I took my solution (well, my refinement of JocK's soution) from the second half of the other thread rmsgrey just linked to above, scaled it up by a factor of two, and added an additional half-circle about the starting point. If there's a shorter curve which is not less than 1 mile from the starting point in any direction, I believe it must be a different solution entirely.
--SMQ
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rmsgrey
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Re: Lost in the woods
« Reply #3 on: Apr 5th, 2006, 5:46am » |
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on Apr 4th, 2006, 6:04am, SMQ wrote:
You sure about that? I don't see a way to do better than [sqrt]3 + 7[pi]/6 + 1 ~= 6.397 miles.
To arrive at that figure I took my solution (well, my refinement of JocK's soution) from the second half of the other thread rmsgrey just linked to above, scaled it up by a factor of two, and added an additional half-circle about the starting point. If there's a shorter curve which is not less than 1 mile from the starting point in any direction, I believe it must be a different solution entirely.
--SMQ |
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Slight nitpick - you're adding only 5/12 of a circle into your solution...
That does seem to be the optimum achievable result though...
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SMQ
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Re: Lost in the woods
« Reply #4 on: Apr 5th, 2006, 6:11am » |
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on Apr 5th, 2006, 5:46am, rmsgrey wrote:
Slight nitpick - you're adding only 5/12 of a circle into your solution... |
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Well, I'm adding 5/12 to what I said, but a full half circle to what I meant.  As Grimbal pointed out in the other thread, when I said "180 degrees" I actually meant "150 degrees". My mistake there was due to the orientation I was picturing the path in my head.
--SMQ
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--SMQ
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Grimbal
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Re: Lost in the woods
« Reply #5 on: Apr 5th, 2006, 7:49am » |
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on Apr 3rd, 2006, 10:17pm, mallman wrote:| Hint: More than one mile less than 6.2 miles. |
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Read that as: More than (one mile less than 6.2 miles).
and not: More than one mile, less than 6.2 miles.
I get the same result as SMQ.
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